To establish transience criteria for a non-local Dirichlet form,
we adopt the so-called Lyapunov method;
that is, we apply some test function to the generator and
use the martingale characterization of the generator.
This method is standard for diffusion processes (see, e.g., [1]} and references therein)
and applicable to jump processes (see, e.g., [2]}).
Here we use this method separately to the generators
corresponding to small and big jump parts.
For the small jump part,
we develop calculation in [3]}
to find the influence of the coefficient growth rate and spatial dimension on transience (Proposition REF ).
Concerning the big jump part,
we need elementary but involved calculation
in order to ensure the existence of a test function (Lemma REF ).
Because of this, we impose a strong restriction on the big jump part
(see Subsection REF ).
Our approach for the big jump part is motivated by [2]}.
